Theorem truthtblfbit-P4.39c 509

Description: ( F ↔ T ) ⇔ F. †

Assertion

Ref	Expression
truthtblfbit-P4.39c	⊢ ((⊥ ↔ ⊤) ↔ ⊥)

Proof of Theorem truthtblfbit-P4.39c

Step	Hyp	Ref	Expression
1		true-P3.44 352	. . . . 5 ⊢ ⊤
2	1	rcp-NDIMP0addall 207	. . . 4 ⊢ ((⊥ ↔ ⊤) → ⊤)
3		ndbier-P3.15.CL 250	. . . 4 ⊢ ((⊥ ↔ ⊤) → (⊤ → ⊥))
4	2, 3	ndime-P3.6 171	. . 3 ⊢ ((⊥ ↔ ⊤) → ⊥)
5	4	ndfalsee-P3.20 185	. 2 ⊢ ¬ (⊥ ↔ ⊤)
6	5	nthmeqfalse-P4.21b 443	1 ⊢ ((⊥ ↔ ⊤) ↔ ⊥)

Syntax hints:   ↔ wff-bi 104  ⊤wff-true 153  ⊥wff-false 157

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155  df-false-D2.5 158

This theorem is referenced by: (None)